1 Answer
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If you type Ctrl-V Ctrl-1 at a shell prompt, you won't get any output (compare to Ctrl-V Ctrl-i, for example).

Running xev, Ctrl-1 gives "1" with a state code signifying that Ctrl is held down, so you may be able to map Ctrl-1 to an unused escape sequence using xmodmap and then map that sequence to the select-window function in tmux.